Memes

That’s only true within the sphere of Marxist ideology and is not a widely-held distinction made by the rest of society. i.e., actual current law wherein:

Private property refers to the ownership of property by private parties - essentially anyone or anything other than the government. Private property may consist of real estate, buildings, objects, intellectual property (copyright, patent, trademark, and trade secrets). The transfer of a private property commonly takes place by the owner's consent or through a sale or as a gift.

Outside of Marxist ideology, and in actual practice, individuals are one class of private entity, making personal property a type of private property. The average person can not be expected to fully understand the nuances of how Marxism alters these definitions, nor accept them in practicality.